KL7UW
Worksheet for OVRO / SBMS EME Test



   SBMS Announces negotiations with Owens Valley Radio Observatory for conducting
   EME Tests using the 40 meter dish:


   Doug Millar, K6JEY, SBMS Project Director
   announced that the San Bernardino Microwave Society
   had gained permission to use the 40m dish at OVRO during the
   2005 ARRL EME Contest.  The dish at OVRO was used during the 
   EME Contest and in late December.

   March, 2006: The SBMS has established a new OVRO Website 
   devoted to the OVRO Project.  Please go there for operating 
   information late breaking news and information about the project.

   Also check out the photos on Greg, KJ6KO's, website.

   The SBMS hopes that this will encourage operation by stations with 
   small 3 or 4-foot dishes and moderate power.


   Skip to the bottom of the page to see tables predicting dish
   performance for a range of dish sizes. 







                [Cal Tech Photo]

Path-Link Analysis: On my 2-meter EME page I gave a link to my EME Path-Link Program for VHF/UHF use. Here is the MW EME Path-Link Program. This should work well for microwave EME analysis. Please try it and provide some feedback on how well it does. Reveiwing assumptions and formula used for eme calculations: The Moon loss formula I used in my original eme spreadsheet was taken from the website of Christoph Petermann, DF9CY, several years ago, and I merely assumed its accuracy extended to microwave frequencies. Examining the formula, I now see that it was a combination of free-space loss with two factors added to correct for spherical losses and lunar surface reflectivity. Free space loss from an isotropic omnidirectional antenna is described by this formula. It calculates the surface area of an imaginery sphere of radius, d, that the radio wave illuminates uniformly: Loss = [ 4*pi*d/lambda]^2 where pi = 3.14, d = distance and lambda = wavelenth, in meters Lambda = c/F F = Hz, c = 3*10^8 meters/sec. Lambda = 300/F when F is in MHz. Substituting F into the free-space loss formula and converting to d into km: Loss = 4*pi*10^3*F*d/300 or Loss(dB) = 32.45 + 20Log(F) + 20Log(d) Adding factors for reflection from the Moon results in Loss-eme(dB) = 32.45 + 20Log(F) + 20Log(2*d) + 50.21 - 10Log(.065) Apparently this formula is sufficient for describing eme loss at VHF/UHF frequencies when the antenna beamwidth is much wider than the apparent angle of the Moon. After I first posted this webpage for analyzing the Lunar path-link for the 40 meter dish, I received some e-mail pointing out that my analysis overlooked some issues that exist for eme at microwave frequencies and as a result it was overly optimistic about expected signal reception. I was referred to the in-depth analysis done by Josef Fehrenbach, DL7FJ: "What's different on10 GHz EME". In his paper, Josef cites the standard radar path-link formula as his basis for eme path-loss calculations: Pr = Pt*Gt*Gr*Loss Loss = rho*lamba^2/(4*pi*)^3 *d^4 after including the factor for surface reflectivity it becomes: Loss-eme(dB) = 100.4 + 20Log(F) + 40Log(d) - 10Log(rho) rho = 0.065*lunar diameter^2*pi/4 since the diameter of the Moon is 3.5*10^6 km rho = 6.25 * 10^11 square-meters. Josef's formula becomes: Loss-eme(dB) = 20Log(F) + 40LOG(d) - 17.49, F = MHz, d = km For some reason not specified, Josef has increased the loss by 3-dB producing: Loss-eme(dB) = 103.4 + 20LOG(F) + 40LOG(d) - 10Log(rho), or Loss-eme(dB) = 20Log(F) + 40LOG(d) - 14.49 I have decided to incorporate this loss formula into my new spreadsheet for mw eme calculations. When comparing results with my original formula there is 3.7 dB less path-loss calculated by Josef's formula. I can't explain this discrepancy. Here is some basic data on the Moon: Moon (perigee) d = 356,400 km, Apparent size = 0.56 deg, 1296-MHz EME Path Loss = 269.8 dB, 10-GHz EME Path Loss = 287.9 dB Moon (apogee) d = 406,700 km, Apparent size = 0.49 deg, 1296-MHz EME Path Loss = 272.1 dB, 10-GHz EME Path Loss = 290.2 dB Difference = 2.3 dB I ran some gain and beamwidth calculations at 1296 and 10,368 MHz for a range of dish diameters (I assumed a dish efficiency of 50% except for the OVRO dish which is 42%):
Parabolic Dish Gain and Beamwidth Calculations at 1.2 and 10.4 GHz
Diam(FT) Diam(M) Gain(1.2) Gain(10.4) HPBW(1.2) HPBW(10.4) 2xHPBW(1.2) 2xHPBW(10.4)
3 0.91 19.9 38.0 18.0 2.25 36.0 4.50
6 1.8 25.9 44.0 9.0 1.13 18.0 2.26
8 2.4 28.4 46.5 6.7 0.84 13.5 1.68
10 3.0 30.4 48.4 5.4 0.68 10.8 1.36
12 3.7 32.0 50.0 4.50 0.56 9.0 1.12
16 4.9 34.5 52.5 3.38 0.42 6.76 0.84
20 6.1 36.4 54.5 2.70 0.34 5.40 0.68
26 8.0 38.7 56.7 2.08 0.26 4.16 0.52
30 9.2 39.9 58.0 1.80 0.23 3.60 0.46
130 40.0 51.9 70.0 0.42 0.05 0.84 0.10
For all the following analysis I assume the following station parameters: Receiver noise temp (1296): Tr = 54 K (system NF = 0.74 dB) Receiver noise temp (10 GHz): Tr = 80 K (system NF = 1.06 dB) Antenna noise temp: Ta = 40 K Cold sky temp (1296): Tc = 10K Cold sky temp (10 GHz): Tc = 5 K Moon temp: Tm = 210K Sky temp: Tsky = f(Tm) + g(Tc) Effective Rx noise Te = Tr + Ta + Tsky Receiver bandwidth B = 200 Hz Receiver Sensitivity Pn = 10LOG(KTeB) Transmitter EIRP Po = Pt + Gt - L(wg), L(wg) assumed to be 0.3 dB Signal to noise ratio S/N = Po + L(eme) + Gr - Pn Examination of the effect of relative illumination of the Moon by an antenna: Josef's paper addresses several factors that impact eme at 10 GHz . These particularly become a concern when analyzing the expected performance of the Owen's Valley 40m dish. In this section I want to discuss some of these concepts and explain the assumptions I incorporated into the new microwave eme path-link analysis program. Factors not considered: Josef covers issues on Doppler "smearing" (broadening of signal due to multipath phase modulation), atmospheric attenuation, Faraday polarization effects, feedhorns, and tracking issues. I chose not to address these, but only to focus on basic signal levels resulting from various combinations of antennas and station parameters. Antenna Beam Power Density: I assume that parabolic dish antennas are used (as does Josef). I also assume that side-lobes are sufficiently suppresssed to not significantly affect performance and that the beam is symetrical in E and H-planes. Furthermore, I have adopted Josef's analysis (figures 6 and 7) which show that most of the the transmitter power is contained within twice the half-power beamwidth. In figure-8, Josef shows path-loss relative to a 4m dish and adds a factor for beam shape. I used the simpler straight-line model in my program, so if one desires more accuracy, they should refer to figure-8 when interpreting the signal levels predicted by my program. Effect of Antenna Beamwidth equal to or smaller than Lunar apparent angle: Considerable calculation is made according to a logic-tree that examines different beamwidth relationships to the apparent Lunar (angular) size, and adding an ERP adjustment where applicable. I call the adjustment IL (illumination loss) and the result EIRPm.
  • Both Tx and Rx antenna beams are wider than the Moon: In this case only a portion of the antenna beam illuminates or sees the Moon. Therefore, there is no affect on the basic path-loss equation.
  • The Tx beam is smaller than the Moon, but the Rx beam equal or wider than the Moon, there is no increase in reflected power by increasing Tx antenna gain beyond the beam that matches the Moon's size. This gain factor is 56-dBi. This results in limiting EIRP at that level for larger dishes: EIRPm = Pt - Lwg + 56
  • The Rx beam is smaller than the Moon - the illumination factor becomes more complex: If the Tx beam is wider or equal to the Moon, there results in a loss by the Rx antenna not seeing all the power illuminating the Moon. A simple ratio of the Rx beam-area to the Moon angular area is used as a correction factor (IL) in the path-loss calculation: EIRPm = EIRP - 20Log (Moon/Rx)
  • If both the Rx and Tx beams are smaller than the Moon, then it matters which is wider. As both antenna beams approach each other in size additional gain results if both illuminating the same spot on the Moon:
  • If the Tx beam is larger than or equal to the Rx beam, the signal received by the Rx antenna is reduced by a factor proportional to the ratio of the beam-areas: EIRPm = EIRP - 20Log (Tx/Rx)
  • If the Tx beam is smaller than the Rx beam, then the EIRP is limited to one from an antenna equal in beamwidth to the Rx antenna: EIRPm = Pt - Lwg + Gr
Effect of Moon Noise on Receiver Sensitivity: We use three noise factors to characterize receiver noise performance (NF): Receiver noise figure or noise temperature, antenna noise temperature (basically ground noise pickup), and sky noise temperature. Good receiver and antenna engineering can reduce the first two factors but sky temperature is given by what the antenna looks at. At microwave frequencies between 1 and 10 GHz this is the basic galactic noise background. The two strongest natural noise sources in the sky are the Sun and Moon. At VHF and UHF frequencies atmospheric noise overwhelms celestial sources, but at microwave the Moon becomes a significant sky noise source especially as antenna beamwidth approaches the angular size of the Moon. I used a simple sky noise model which compares the ratio of Moon area to total beam area and uses a Moon temperature of 210 K and cold sky noise based on a frequency table. When the antenna beam is equal or less than the size of the Moon, Tsky = 210 K. This affects receiver sensitivity (Pr), significantly, and that can result in a reducing the overall SNR achieved by larger dishes. The following case-studies use the new path-link program to examine a few antenna combinations. I added a table at the end to explore expected performance with the 40 meter OVRO dish. Case Studies: CASE-I: Two 10-foot dishes running EME at 15w transmitted power: We start with a ten-foot dish with 15 watts that is considered the current norm for 10-GHz EME (from Barry, VE4MA). Using the standard station parameters from above:
  • Since the Moon only partially fills the beam of the antenna: Tsky = 40.3 K and Te = 160.2 K; Pn = -153.5 dBm
  • Since both Rx and Tx antennas have beamwidths that are larger than the Moon, no corrrection for Illumination is needed: antenna gain is 48.4 dBi and EIRP = 88.1 dBm
  • SNR = EIRP + Path Loss + Rx antenna gain - Receiver sensitivity (Pn)
  • SNR = 3.9 dB for Moon at perigee and is 1.6 dB at apogee. This will show a good EME signal using CW (since most operators can copy CW to - 6 dB S/N).
CASE-II: Two 20-foot dishes running EME at 10w transmitted power : The remaining cases will use a transmitter power of 10 watts, since this is what is planned for at OVRO and is fairly common amongst non-eme microwavers using low-power TWTA's. This will make comparisons easier in the final table.
  • Twenty-foot dishes exhibit higher gain and beamwidths that almost match the Moon.
  • Tsky = 149 K, Te = 268.8 K, and Pn = - 151.3 dBm; about 2 dB worse receiver sensitivity due to Moon noise.
  • Antenna gain is 54.5 dBi and EIRP = 94.2 dBm with no correction for illumination.
  • SNR = 12.1 dB is a very strong signal for CW on the Moon; just about the two-times the 6-dB gain over the ten-foot dishes, as one would expect after adjusting S/N by 1.8 dB for reducing Pt from15w to 10w.
CASE-III: A 6-foot dish running 10w, working EME with a 12-foot dish: This is the case where a small dish works a medium-sized dish. Still both dish beamwidths are wider than the Moon, so no illumination adjustments were required.
  • Tsky for the small dish is 17.8 K vs the 56.1 K of the larger dish resulting in 1.1 dB better sensitivity with the smaller dish receiver.
  • Antenna gain 6 dB greater for the twice as large dish resulting in EIRP = 89.7 dBm vs 83.7 dBm.
  • SNR = - 1.1 dB for the large dish, while for the smaller dish SNR = 0.0 dB reflecting the better Moon noise.
CASE-IV: A 6-foot dish running 10w, working EME with a 30-foot dish: Now we will explore the combination of a dish with a beamwidth much wider than the Moon with one that is narrower than the Moon. Moon illumination will need adjustment with this pair of antennas.
  • First of all the 9.2 meter dish see's only the Moon so Tsky = 210 K. Its receiver sensitivity is - 150.4 dBm nearly 4 dB worse than the small dish.
  • EIRP of the big dish is limited to 56 dB since the extra gain does not benefit the small dish reception since the big dish beamwidth is smaller than the Moon. Likewise the EIRP of the small dish is reduced since the big dish does not see all the Moon and misses power illuminating the edge of the Moon; a shared penalty of 4 dB.
  • SNR = 6.0 dB for the small dish and 2.2 dB for the big dish, mainly the result of Moon noise in the Rx.
CASE-V: A 3-foot dish running 10w, working EME with the 130-foot OVRO Dish: Now we get to the example that the SBMS is hoping will enable small non-eme microwave stations to accomplish. A small 3-foot dish working the large 40 meter Owen's Valley Radio telescope. Severe under illumination penalties occur:
  • Tsky = 210 K for the 130-foot dish and 8.2 K for the 3-foot dish, producing a receiver sensitivity difference of 4.1 dB!
  • EIRP of the big dish is held to 95.7 dBm (a 14 dB penalty) making it no more effective than a 24-foot dish. The EIRP of the 3-foot dish is similarly reduced to 63.74 dBm (by roughly 14 dB) due to the OVRO 0.1-degree beam not seeing all the energy that the small dish is radiating to the lunar surface.
  • The SNR received by the small dish is still useful at 0.3 dB; the SNR at the big dish is only - 3.8 dB so probably very marginal copy. The only way to improve their SNR is if the small station can generate more power. Running 25w will raise the SNR = 0.2 dB, equalizing the exchange.
CASE-VI: A 4-foot dish working 1296-MHz EME with the 130-foot OVRO Dish: I thought I would add one calculation for 1296-MHz. SBMS plans to operate with a 100 watt transmitter. I will use 20w for the small dish station as that power is easily achieved. The 4-foot dish is perhaps too small (that is only 5 wavelengths) for efficient use at 1296-MHz, so one should consider that the results may be optimistic. (Note: a single long loop-yagi may perform as well).
  • I assumed that the preamp for both stations is placed at the feed using a hybrid for circular polarization and that the convertor/receiver may be a long coax run (- 6 dB) at the ground giving Tr = 74 K, Ta = 40 K, Tsky = 10.1 K for the small dish and Tsky = 101.9 K for the OVRO dish.
  • Receive sensitivity is -155.4 dBm for the small system and -152.7 dBm for OVRO. Again the plenalty is for seeing more Moon noise.
  • EME path-loss at perigee is 269.8 dB with EIRP = 101.6 dBm (OVRO) and 65.1 dBm for the small dish. Both antennas over-illuminate the Moon so no correction factor applies.
  • SNR = 9.6 dB on the small dish system and SNR = - 0.2 dB at OVRO, thus possible for EME.
TABLES: Comparison of several size dishes working EME with the 40m OVRO Dish:
1296-MHz EME with OVRO 40m DISH
OVRO: Tsky = 101.9 K, Pr = -152.7 dBm, Pt = 100w, EIRP = 101.6 dBm, IL = 0 dB, EIRPm = 101.6 dBm
DISH SIZE HPBW GAIN Tsky Pr EIRP ILLUM L EIRPm SNR OVRO SNR
4-FT (1.2m) 13.5 22.4 10.1 K - 155.4 65.1 0.0 65.1 + 9.6 - 0.2
6-FT (1.8m) 9.0 25.9 10.2 K - 155.4 68.6 0.0 68.6 + 13.1 + 3.3
8-FT (2.4m) 6.7 28.4 10.3 K - 155.4 71.1 0.0 71.1 + 15.6 + 5.8
10-FT (3.0m) 5.4 30.4 10.5 K - 155.4 73.1 0.0 73.1 + 17.5 + 7.8
12-FT (3.7m) 4.5 32.0 10.8 K - 155.4 74.7 0.0 74.7 + 19.1 + 9.4
16-FT (4.9m) 3.38 34.5 11.4 K - 155.4 77.2 0.0 77.2 + 21.6 + 11.9
20-FT (6.1m) 2.7 36.4 12.2 K - 155.3 79.1 0.0 79.1 + 23.5 + 13.8
26-FT (8.0m) 2.08 38.7 13.7 K - 155.3 81.4 0.0 81.4 + 25.7 + 16.1
30-FT (9.2m) 1.8 39.9 14.9 K - 155.2 82.6 0.0 82.6 + 26.9 + 17.3
10-GHz EME with OVRO 40m DISH
OVRO: Tsky = 210 K, Pr = -150.4 dBm, Pt = 10w, EIRP = 109.7 dBm, IL = 14 dB, EIRPm = 95.7 dBm
DISH SIZE HPBW GAIN Tsky Pr EIRP ILLUM L EIRPm SNR OVRO SNR
3-FT (91cm) 2.24 38.0 8.2 K - 154.5 77.7 14.0 63.7 + 0.3 - 3.8
6-FT (1.8m) 1.13 44.0 17.8 K - 154.2 83.7 14.0 69.7 + 6.0 + 2.2
8-FT (2.4m) 0.84 46.5 27.8 K - 153.9 86.2 14.0 72.2 + 8.2 + 4.7
10-FT (3.0m) 0.68 48.4 40.3 K - 153.5 88.1 14.0 74.1 + 9.7 + 6.6
12-FT (3.7m) 0.56 50.0 56.1 K - 153.1 89.7 14.0 75.7 + 10.9 + 8.2
16-FT (4.9m) 0.42 52.5 95.8 K - 152.3 92.2 14.0 78.2 + 12.6 + 10.7
20-FT (6.1m) 0.34 54.5 149 K - 151.3 94.2 14.0 80.2 + 13.6 + 12.7
26-FT (8.0m) 0.26 56.7 210 K - 150.4 96.4 13.3 83.1 + 15.6 + 15.6
30-FT (9.2m) 0.23 58.0 210 K - 150.4 97.7 10.0 85.7 + 18.2 + 18.2
I would appreciate your comments or corrections. Return to Homepage page